1 - It is normally difficult to obtain insurance without having a US license. Some insurance companies will allow you to start a policy with your foreign license and give you time, around 30 to 45 days, to acquire a State license or else cancel your policy. If you are going to be staying in the United States for graduate studies at a college or university then it likely will not be too difficult for you to get a state's driver's license.

2 - Your brother may be able to add you to his insurance policy as an additional driver depending upon the guidelines of his insurer. Likely they will require you to obtain a US license as well. If your brother can add you to his policy online will depend on his specific insurance provider and if this type of policy change is available to do online with them.

3 - Yes, a car registered in one state is allowed to be driven in other states. If you are going to be the owner of the car and live in a state other then Wyoming the car may need to be registered there.

Keep in mind that state laws as well as insurance company guidelines differ so you may need to check with the state in which you plan to dwell in for addition information. If you are going to be going to school and residing in Wyoming, check with the Driver Services of the WY Department of Transportation to see about how to go about getting a driver's license in their state.